The V&A director, Tristram Hunt, has said the museum was “honoured” to have the financial support of the billionaire supporter of Donald Trump Len Blavatnik, and welcomed it from donors of “all political views and no political views”.

Hunt on Wednesday launched the museum’s annual review, announcing exhibitions on a diverse range of subjects including Frida Kahlo, video games, and the environmental impact of fashion.

“We regard him as a very generous patron and supporter of the arts and what his political views are – that’s a question for him. In terms of the support for arts and culture we are just very grateful for his support.”

Hunt, a historian and former Labour politician who was appointed V&A director this year, said a donor’s politics were not a concern.

Rothstein said he had received hundreds of messages of support after resigning his Oxford professorship in protest at Blavatnik giving money to Trump’s inauguration. In his resignation letter he wrote: “President Trump stands for a system of governing that is completely contrary to what I have come to define as ‘quality of government’.”

Blavatnik denies donating to Trump. Instead the money was to the committee that had been responsible for organising US presidential inaugurations since 1901.

He also denies being an associate of Putin and has stated that he has had no personal contact with the Russian leader since 2000.

Hunt, who has not met Blavatnik, said the businessman’s money was welcome and had helped fund the new Exhibition Road Quarter, the museum’s largest architectural innovation in more than 100 years, providing the new entrance and a new temporary exhibition space, the Sainsbury Gallery.

The design for the V&A’s new Exhibition Road Quarter. Photograph: Hufton+Crow

In 2018 the gallery will be used for a major exhibition called The Future Starts Here, exploring how design is “shaping the world of tomorrow” whether through smart appliances, satellites or artificial intelligence.

The V&A’s big autumn show will be on video games, said Hunt, describing it as “the first in the world to fully consider the complexity of video games as one of the most important design fields of our time”.

There will be large immersive multimedia installations, as well as the opportunity to play.

Hunt said the V&A was the ideal home for video games. “We are very happy to have them in the same building as Donatellos, Botticellis, Christopher Dressers and Constables and Turners. One of the challenges for the V&A is to get people to think differently about what they might not respect enough visually.”

The V&A has long been known for the diversity of its exhibition programme and that continues in 2018 with a show on the environmental nature of fashion, sponsored by the European Confederation of Linen and Hemp; the first exhibition outside Mexico of clothing and personal possessions of Frida Kahlo, which were discovered in 2004 in sealed cupboards and storerooms; and previously announced shows on Winnie-the-Pooh and ocean liners.

When Tristram Hunt stepped down as an MP in order to lead the V&A, critics were quick to ask what qualified him for the role. Of course he’s qualified, he argues – and no, he won’t answer political questions